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A Note on Uniform Interpolation Proofs in Modal Deep Inference Calculi

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Logic, Language, and Computation (TbiLLC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6618))

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Abstract

This paper answers one rather particular question: how to perform a proof of uniform interpolation property in deep inference calculi for modal logics. We show how to perform a proof of uniform interpolation property in deep inference calculus for the basic modal logic K via forgetting a variable in a certain normal form constructed by backward proof search. For that purpose we modify the framework of deep-inference calculus using a cover modality on the meta level to structure deep sequents.

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Authors and Affiliations

  1. Institute of Computer Science AS CR, Pod Vodárenskou věží 2, 182 07, Prague 8, Czech Republic

    Marta Bílková

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  1. Marta Bílková
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Editors and Affiliations

  1. Department of Computing, Imperial College London, 180 Queen’s Gate, SW7 2AZ, London, UK

    Nick Bezhanishvili

  2. Institute of Language and Information, Department of General Linguistics, Heinrich-Heine-University, Universitätsstraße 1, 40225, Düsseldorf, Germany

    Sebastian Löbner

  3. Zentrum für Allgemeine Sprachwissenschaft, Schützenstraße 18, 10117, Berlin, Germany

    Kerstin Schwabe

  4. Dipartimento di Matematica, via Ponte don Melillo, 84084, Fisciano, (SA), Italy

    Luca Spada

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Bílková, M. (2011). A Note on Uniform Interpolation Proofs in Modal Deep Inference Calculi. In: Bezhanishvili, N., Löbner, S., Schwabe, K., Spada, L. (eds) Logic, Language, and Computation. TbiLLC 2009. Lecture Notes in Computer Science(), vol 6618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22303-7_3

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  • DOI: https://doi.org/10.1007/978-3-642-22303-7_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22302-0

  • Online ISBN: 978-3-642-22303-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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